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Cao, H, Amador, C, Jia, X et al. (1 more author) (2015) Capillary Dynamics of Water/Ethanol Mixtures. Industrial and Engineering Chemistry Research, 54 (48). pp. 12196-12203. ISSN 0888-5885

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1

Capillary dynamics of water/ethanol mixtures

Hui Cao1,*, Carlos Amador2, Xiaodong Jia3 and Yulong Ding1

1School of Chemical Engineering, University of Birmingham, B15 2TT, United Kingdom

2 Procter & Gamble Newcastle Innovation Center, Newcastle Upon Tyne, NE12 9TS, United

Kingdom

3School of Chemical and Process Engineering, University of Leeds, LS2 9JT, United Kingdom

Corresponding Author*h.cao@bham.ac.uk

ABSTRACT Surface tension and contact angle play important roles in capillary dynamics during

washing commission of spray-dried detergent powder where interaction between surface

chemistry and liquid is concerned. An experimental study for the dynamics of water/ethanol

mixtures in both hydrophilic and hydrophobic capillary tubes has been investigated. The

combination of water/ethanol mixtures and Trimethylchlorosilane coating on capillaries provides

a variety of liquid surface tension and contact angle for the penetrating system. Significant

differences of penetrating speed on hydrophilic and hydrophobic tubes indicate that dynamic

contact angle dominates hydrophobic surface while liquid surface tension plays a more important

role on hydrophilic surface. The speed gradient of different liquids on hydrophilic surface is

greater than hydrophobic surface, mainly due to the domination between hydrogen bonding

2

structures and water polarity while liquid moves on surfaces covered with different chemistry,

physically absorbed water on silica capillaries or silanol groups covered capillaries.

KEYWORDS Capillary dynamics; Silylation; Hydrophilic; Hydrophobic; AFM

1. INTRODUCTION

Porous media can be characterized by studying the kinetics of liquid rise within the pore spaces1.

The penetration of liquids into porous materials due to capillary action is important in a wide

range of technological fields such as agriculture, oil recovery, pharmaceutics, chemical

engineering and civil engineering2-4. A porous medium is a complicated system of connected

pores, and in most of the case these pores have rough walls and throats which makes the study of

capillary mechanism critically relevant. The kinetics of the penetration in these pores is

considered to be influenced mainly by its structure (pore geometry, surface roughness etc.) and

the wettability of the constituent pores. However, due to scale and imaging limits, investigation

of flow kinetics in these random porous medium is very difficult at pore-level. Instead, using

glass micromodels and capillary tubes can simplify this study while providing informative

parameters which are difficult to probe directly in these naturally random porous medium.

Kinetics of liquid rise in single capillary tubes was formulated almost at the same time by

Lucas5, Washburn6, and Rideal7 in the early 20th century. Assuming contact angle of fluid

meniscus during displacement was constant, Washburn derived fluid flow equation in capillary

tubes using Poiseuille's law6 and suggested that penetrating length is proportional to root time.

Quere reported an linear relationship during early stages of rise by experiment8 and observed

oscillations around the equilibrium stages when the liquid viscosity is low enough9. The author

3

along with other researchers1, 10-11 proved that dynamic contact angle should be implemented in

Washburn's equation in order to make a better agreement between experimental data and

equation predictions. Hence, an intensive collection of dynamic contact angle in different

capillary system is essential for scientists to improve the theoretical prediction.

Spray-dried detergent powder normally is considered as random porous medium. Due to process

differences and formulation divergences, the surface chemistry of spray-dried detergent powders

has a variety wetting properties to water. From industrial application's point of view, it is

imperative that investigation of water penetrating into these porous medium during washing

commission and understanding how capillary dynamics influence the performance of detergent

powder to be carried out. A detailed investigation of the action between the surface chemistry of

capillary and liquid molecular regarding the capillary flow dynamics is of more interesting to

researchers. There have been several experimental investigations on the effects of velocity and

capillary number on dynamic contact angle, and empirical correlations have been developed

since then12-16. Not until very recently, an extensive, well-characterized experimental study of

dynamic contact angle changes with meniscus velocity in capillary rise experiments for different

fluid systems has been reported17. However these works have very limited information of

statistic experimental data sets especially for liquids with different surface tension and contact

angle in capillaries where surface chemistry is concerned. Few researchers reported capillary

kinetics of liquid penetrating into different surfaces without concerning contact angle changes.

An earlier paper focused on penetration rate, wetting force and surface free energy changes when

water/ethanol mixtures penetrating into silanized silica fibrous assemblies by measuring

electrical conductivity18. But their results lack information of mixture penetration behaviour and

the relatively parameters to guide the development of predictive models. Bain reported

4

penetration kinetics of surfactant solution on hydrophobic capillaries assuming dynamic contact

angle is equal to equilibrium contact angle19. Starov20 presented a theoretical model trying to link

contact angle with aqueous surfactant solution where contact angle is always bigger than 90°. To

the best of our knowledge, there are very limited number of experimental data sets available in

the literature that can be used to characterize the variation of dynamic contact angle in a system

where surface chemistry on the capillary tube has been concerned. Therefore, the extent and

quality of the experimental data on this interfacial parameter are highly desirable for the

predictive capabilities of the models that one can develop and potentially in the future to predict

capillary actions on detergent powder during washing commissions.

In the present study, penetration rates of water/ethanol mixtures into hydrophilic and

hydrophobic capillary tubes have been investigated considering different surface tension and

contact angle effects. Glass tubes were treated with silane coupling agents to modify the surface

chemistry of the capillary first. Then Atomic Force Microscope (AFM) was used to observe

surface structure changes before and after silane treatment. The advancing meniscus of liquid

was recorded by high speed camera and videos were analysed by ImageJ to extract the

penetration height as a function of time. Detailed discussion about the action between hydroxyl

groups (OH) on capillary surface and inside liquid has been presented regarding the capillary

flow dynamics. Dynamic contact angle changes in both hydrophilic and hydrophobic capillaries

was plotted based on the calculation from empirical equations.

2. EXPERIMENT

2.1. Materials

5

Capillaries. Capillaries with three different inner radius purchased from World Precision

Instruments Ltd were used in the experiments, 0.34 mm, 0.45 mm and 0.56 mm. Before

experiment, the capillaries were first embedded in pure ethanol and ultrosonicated for half an

hour to remove the remains. Then they were flushed by deionised water, rinsed in deionised

water and ultrosonicated for another half an hour. At last, they were dried in clean air atmosphere

at 60°C for 12 hours. Hydrophobic capillaries were obtained by exposing clean capillaries to

Trimethylchlorosilane (Sigma-Aldrich, purity > 99%) for 12 hours at room temperature, which

then reacted with the silanol groups on glass tube surface. The capillaries were stored at 20°C

separately in desiccators with silica gel and were exposed to 20°C and 65% relative humidity

prior to use.

Chemicals. Deionised water and pure ethanol were mixed with different ratio as showing in

Table 1.

2.2. Methods

Capillary dynamics. The capillary rise dynamics was followed from the moment when capillary

tube contacted the liquid and stopped when liquid meniscus balanced at certain height. First,

liquid was placed in a cylindrical glass dish filled slightly over the rim to allow imaging

immediately when the capillary tube touched the liquid. Fast rise processes were recorded by a

high speed camera (FASTCAM SA 5, Photron Ltd) connected to a computer. The camera was

set up at 2000 frames per second. The images were analysed by software ImageJ. The schematic

was shown in Figure 1.

Surface morphology. The inner surfaces of capillaries before and after coating process were

scanned by AFM in order to investigate the effect of coating process on surface morphology.

6

Physical properties. Physical properties of the liquids were measured, including density,

viscosity and surface tension, by a Density Meter (DMA Generation M, Anton Paar), a

Rheometer (MCR Series, Anton Paar) and a Contact Angle Measuring System (EasyDrop,

KRUSS), respectively. Results are listed in Table 1.

3. RESULTS AND DISCUSSION

3.1. Atomic morphological studies

Wettability of a solid surface to a certain liquid is governed by two factors, i.e. a chemical factor

and a geometrical factor of the surface21-23. Barthlott and Neinhuis first reported that both surface

microstructure and chemical composition of a solid surface can determine its hydrophobicity24.

Later on, researchers further studied by finely controlling the micro/nanostructure or chemical

composition of a surface, the contact angle of water on this surface can be manipulated between

hydrophilic and hydrophobic25-28.

Silylation is a popular process to change a hydrophilic surface into hydrophobic property25. In

this study, we coated TMCS on capillary tubes to change the surface chemistry. Figure 2 and

Figure 3 are typical AFM images of the unmodified and TMCS modified glass tube inner

surface, respectively. The images were recorded at 2 µm planar in contact mode. Figure 2 (a)

and Figure 3 (a) are two dimensional (2D) images, and Figure 2 (b) and Figure 3 (b) are three

dimensional (3D) images. In 2D images, Figure 3 (a) shows slightly bigger

dotfeaturescomparing to Figure 2 (a). And in 3D images, these peak features in Figure 3 (b) are

rougher than Figure 2 (b) which indicates a higher surface roughness. The root-mean-square

(RMS) roughness values of the films analysed by AFM show that the surface roughness of

TMCS modified glass tube is twice as the unmodified one, with a RMS roughness value of 7.8

7

nm and 15.1 nm, respectively. AFM results show that the process of TMCS coating on glass tube

surface does change the surface topography in a considerable level. Surface roughness has a

influence on both the contact angle itself and its hysteresis. An important aspect is the length

scale involved. For roughness significantly below the wavelength of light, which is the case here,

the effect of surface roughness can be described by the so-called Wenzel equation29. The

equation predicts that if a molecularly hydrophobic surface is rough, the appearance is that of an

even more hydrophobic surface. If a hydrophilic surface is roughened it becomes more

hydrophilic29. The coating layer on capillary surface nearly doubles the roughness, which from

the morphology point of view should enhance the hydrophilicity. However, since the silanol

groups are hydrophobic, capillary tubes become hydrophobic consequently.

3.2. Fundamental equations of capillary dynamics

As applied to a viscous noncompressible liquid in a long cylindrical capillary, the Newton

dynamics equation can be expressed as30

貢岷月月旺旺 髪 岫月旺岻態峅 噺 態追 紘 cos 肯 伐 腿追鉄 航月月嫗 伐 貢訣月, (1)

where と is the density (kg/m3) , µ is the viscosity (Pa·s), け is the surface tension (N/m), し is the

contact angle of the liquid (°), h is the height of capillary rise (m), r is the capillary radius (m),

and g is the standard gravity (m/s2). The equation assumes the Poiseuille flow profile throughout

the capillary. The capillary liquid will rise to an equilibrium level, heq, established by the balance

of gravity and capillarity31

月勅槌 噺 態廷 達誰坦提賑忍諦直追 , (2)

8

where しeq is the equilibrium contact angle. By measuring the equilibrium height of each

penetration through the video of high speed camera, using Eq. (2), しeq can be calculated.

A simplified equation derived from Eq. (1), gives the rate of liquid penetration into a

perpendicular capillary as follows5-6:

月 噺 謬廷追態禎 cos 肯 建, (3)

in which the height of capillary rise h ~ t1/2. This is the famous Lucas-Washburn equation. It is

well known that in this equation, some terms for example the gravity effects, the kinetic effects,

the viscous loss in liquid below the tube, and the viscous loss associated with the entrance

effects, have been neglected32. A more detail report showed that capillary rise of low viscosity

liquid in a vertical tube can be characterized into three regimes: i) pure acceleration regime, h ~

t2, ii) linear regime, h ~ t, and iii) Washburn regime, h ~ t1/28, 16-17, 27. Moreover, as mentioned

previously, the contact angle in Eq. (3) should be dynamic contact angle.

3.3. Experimental results of capillary penetration

Capillary tubes with three inner radius of 0.34 mm, 0.45 mm and 0.56 mm were used to perform

the experiments while liquids in Table 1were assisted. Figure 4 shows images captured by high

speed camera. The movement of meniscus were clearly captured by the experiment set up in

Figure 1. After using ImageJ to analyse all the videos, Figure 5 and Figure 6 show the

penetration height verses penetration time which is plotted as log 10 in order to magnify the

differences. Figure 5 is hydrophilic surface and Figure 6 is hydrophobic surface. Obviously,

three regimes are detected throughout capillary tube sizes for both hydrophilic and hydrophobic

surface, which is very similar to literature17. Besides, water does not rise up to hydrophobic

9

capillary tube at all suggesting that the contact angle for water on TMCS modified surface is

greater than 90°. Meanwhile, ethanol and ethanol/water mixture can still go into hydrophobic

tubes.

By comparing Figure 5 and Figure 6, it is clear that flow dynamics in hydrophilic tubes is

different from hydrophobic tubes. For hydrophilic ones, with more ethanol in the liquid, the

equilibrium time and height heq, and penetration speed all decrease. While in hydrophobic ones,

it is the opposite. With increasing ethanol ratio in the liquid, equilibrium height heq and

penetration speed increase explicitly, and slightly for the penetration time.

The equilibrium height as a function of ethanol volume ratio in water is plotted in Figure 7. On

hydrophobic capillary, low volume ethanol mixtures have lower equilibrium height than high

volume ethanol mixtures which is in the opposite direction of hydrophilic capillary. In

hydrophilic surface, with increasing ethanol content in mixtures, the equilibrium height reduces

61%, 61% and 64% on 0.34 mm, 0.45 mm and 0.56 mm capillary tube respectively. In

hydrophobic surface, while ethanol volume increase from 20% to 100%, the equilibrium height

on 0.34 mm, 0.45 mm and 0.56 mm capillaries increases 159%, 140% and 170% respectively.

From Table 1, it is clear that surface tension of the liquid reduces nearly 70% from water to

ethanol, which is nearly the deduction of equilibrium height in hydrophilic capillaries, implying

that surface tension governs in hydrophilic capillary dynamics. While in hydrophobic capillary,

as surface tension decreases from 20% to 100% of ethanol volume in liquid, the equilibrium

height increase drastically. By taking the two aspects, i.e. liquid surface tension and contact

angle, it is likely that a large drop in contact angle occurred from 20% ethanol to 100% ethanol

in hydrophobic capillaries.

10

It is also seen that throughout the experiment, some oscillation occurred around the equilibrium

status. This phenomenon was reported and studied by researchers before1, 9, 30. It was shown that

kinetic force is the main reason that may cause the oscillation of liquid column. As liquid rises

up in capillary, viscous force damps the oscillatory energy out, which leads to an oscillatory

behaviour at the liquid front around the equilibrium height (also called Jurin height)9. The critical

radius, Rcr, can be determined by32:

迎頂追 噺 に 峙禎鉄廷 達誰坦提賑忍諦典直鉄 峩迭天. (4)

The equation indicates if R>Rcr, the kinetic force is strong enough to rise liquid up the

equilibrium height, which leads to oscillation around Jurin height. According to Eq. (4), the

value of critical radius Rcr in silica capillaries, for water is 0.47 mm, for ethanol is 0.45 mm, and

for the mixtures are between 0.56 mm and 0.63 mm. In Figure 5 (a) where capillary radius is

0.34 mm, no oscillation was observed around the equilibrium height. In Figure 5 (b) while

capillary radius is 0.45 mm, a very invisible oscillation occurred on ethanol which can be

neglected. However in Figure 5 (c) while capillary radius is 0.56 mm, a slightly visible

oscillation happened around the Jurin height for both water and ethanol. Similar phenomena

happened again in hydrophobic capillaries.

3.4. Advancing contact angle

Researchers have proposed that during capillary rise process, the contact angle し in Eq. (1)

changes significantly before the meniscus stabilize, which could dominate the process10, 31, 33.

Consequently, dynamic contact angle しad should be used in Eq. (1) instead of constant value or

equilibrium contact angle for any model prediction. Predicting results of Eq. (1) using

11

equilibrium contact angle are compared to experiment results in 0.34 mm radius tube for both

hydrophilic and hydrophobic surfaces, showing in Figure 8. On both hydrophilic and

hydrophobic capillaries, predicting results show higher penetrating speed than experiment result.

Dynamic contact angle on most surfaces exhibits hysteresis, i.e. the advancing and receding

contact angles are different. For the capillary rising case, advancing contact angle plays

important role and should be used in Eq. (1)34.

The dynamic contact angle is dependent on the velocity of the moving meniscus, or capillary

number. Over the last several decades, researchers have introduced various semi empirical

correlations to describe the velocity-dependence of dynamic contact angle12-15. A proposed

accurate empirical correlation is given by13, 16

cos 肯銚鳥 噺 cos 肯勅槌 伐 に盤な 髪 cos 肯勅槌匪系欠怠 態斑 , (5)

where系欠 噺 禎廷 v is the capillary number, and v is the velocity of contact line which can be

calculated by derivating the rise-versus-time curves in Figure 5 and Figure 6. The calculated

advancing contact angle is plotted against capillary number as showing in Figure 9.

The general distribution of advancing contact angle in hydrophilic tubes is quite different from

hydrophobic tubes. Figure 9 (a) shows the variation of advancing contact angle with capillary

number for displacement of air by different liquid in hydrophilic tubes with 0.34mm, 0.45mm

and 0.56mm inner radius. The results are very comparable to the direct image measuring data

reported by Heshmati and Piri17. Figure 9 (b) shows the variation of advancing contact angle in

hydrophobic tubes. It is clearly shown that for the same liquid, advancing contact angles in three

different sized tubes have very similar distribution. As indicated in Eq. (5), advancing contact

12

angle is mainly related to equilibrium contact angle and capillary number. For different sized

capillary tubes, especially those used in this study, the equilibrium heights are similar in most of

the cases except for pure water in hydrophilic tubes (see Figure 7), which result in similar

equilibrium contact angles (Eq. (2)). Hence, advancing contact angles for the same liquid in

different sized capillaries share similar values across capillary numbers.

However, for different liquid, advancing contact angle shows strong relevant to capillary number

in hydrophilic system, and gradually less relevant with decreasing ethanol volume ratio in liquid

in hydrophobic capillaries. It is also noticeable that ethanol volume ratio in hydrophilic surface

has much less effect on contact angle comparing to hydrophobic surface. With more water in the

liquid, advancing contact angle varies from 20° to nearly 80° at low capillary number area. This

is probably due to the silanol groups of TMCS coating on capillary surface make it very water

repellent. The advancing contact angle results confirmed our previous suspect that in the

hydrophilic surface, liquid surface tension dominants the flow dynamics, while in the

hydrophobic surface, advancing contact angle plays a more important role in the flow dynamics.

It is noteworthy that the advancing contact angle for a given capillary number shows, weak

sensitivity to the type of fluid system in a hydrophilic surface. While in the hydrophobic surface,

strong relevant has been observed. This may have important implications for development of

modelling tools used to predict flow at the pore scale in porous media.

3.5. Wettability of hydrophilic and hydrophobic capillaries

In Figure 10, the wetting force in the advancing scan, けcosしad, is plotted against the volume ratio

of ethanol in the liquid at time t =0 s which is the initial stage of capillary penetrating on

hydrophilic and hydrophobic surfaces while tube radius is 0.34 mm. The value of けcosしad

13

decreased with increasing ethanol concentration for the unmodified capillary tube, and increased

for TMCS modified capillary tube, which is consistent with the literature18. Especially on

hydrophilic surface, with additive of ethanol in liquid, wetting force decreases drastically

comparing to pure water. Such a result is more significant by comparing the hydrophilic

penetrating behaviour to the hydrophobic results in Figure 5and Figure 6. The difference of

penetration speed for different ethanol/water mixtures of the hydrophobic one is much greater

than the hydrophilic one. This is probably caused by the silanol groups on the hydrophobic

surface.

Studies shows that a layer of physically absorbed water molecular presents on the surface of

silicates and silicas35-36 and makes them hydrophilic initially. After being coated by TMCS, a

layer of hydrophobic TMCS was formed on the tube surface and nearly doubled the surface

roughness, as illustrated by AFM results in Figure 2 and Figure 3. Different chemistries on

capillaries surfaces cause different penetrating behaviour. For the case of pure water in the

unmodified capillary, water can easily form hydrogen bond to the physically absorbed water on

the silica surface and rise up in the tube continuously until equilibrium. On TMCS coated

surface, it is difficult for water to form any bond to TMCS functional groups. Besides, water is a

highly polar molecule, and TMCS is an organic material with low polarity. As a result water

does not rise up in the tube.

Each sp3 hybridized oxygen atom can form four approximately tetrahedrally disposed hydrogen

bonds in liquid water37. Similar to water, ethanol can be regarded as having a sp3 hybridized

tetrahedral oxygen38.Since the oxygen atom of an ethanol molecule carries one proton and two

lone pairs of electrons, it might form three hydrogen bonds with its neighbors - another ethanol

molecule or a water molecule38. As a result, water and ethanol can form different hydrogen-

14

bonding structures. For the case of pure ethanol in unmodified capillaries, similar to water,

ethanol can rise up in the tube by forming hydrogen bonds with the pre-absorbed water on the

tube surface. For the case of pure ethanol in TMCS modified capillaries, due to its less polarity

and same organic group (CH3) to TMCS, ethanol can also rise up in the tube. The results in

Figure 10 show that ethanol has very similar wetting force on both silica and TMCS coated

capillaries, hence very similar penetration behaviour.

The case of water/ethanol mixtures is more complicated. As discussed above, water and ethanol

can mix freely by forming different hydrogen bonds between each other. When increasing

ethanol concentration in the mixtures, especially after 40 vol%, since ethanol is statistically twice

as likely to act as a proton acceptor than as a donor, ethanol is more dominant than water in the

mixture38. Consequently, wetting forces of different water/ethanol mixtures on both silica and

TMCS coated capillaries are eventually close to the value of pure ethanol. One exceptional case

is ethanol at 20 vol %. On both hydrophilic and hydrophobic tubes, wetting force is either

significantly higher or smaller than pure ethanol which gives indication that in this mixture, the

polarity of water still plays an important role comparing to the hydrogen bond structures.

4. CONCLUSIONS

Although identified 200 years ago, wetting still lives and bounces constantly thanks to new

questions—often arising from practical consideration. The dynamics of water/ethanol mixtures

in both silica capillary tubes and silylated silica capillary tubes has been investigated with

various tube radius by high speed camera at 2000 frames per second. The AFM results indicate

that the silylation process on silica capillary tubes nearly doubles the surface roughness while

surface chemistry has been change (from hydrophilic surface to hydrophobic surface) which also

15

been proved by the capillary penetration results. The gradient of penetrating speed for different

water/ethanol volume ratio is greater on the TMCS treated capillaries than silica capillaries.

Dynamic contact angle calculated from empirical equation based on penetrating results show that

in hydrophilic surface, liquid surface tension dominate capillary rise, while in hydrophobic

surface, contact angle plays a more important role. Drastic drop of wetting force with additive of

ethanol in liquid explained that domination between hydrogen bonding structures and water

polarity is the key reason for different penetration behaviour in the system.

ACKNOWLEDGMENT

The authors would like to give their acknowledgement to Procter & Gamble Ltd., Newcastle

Technical Centre for the research support.

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(32) Masoodi, R.; Languri, E.; Ostadhossein, A., Dynamics of liquid rise in a vertical capillary tube. Journal of Colloid and Interface Science 2013,389 (1), 268. (33) O’Loughlin, M.; Wilk, K.; Priest, C.; Ralston, J.; Popescu, M. N., Capillary rise dynamics of aqueous glycerol solutions in glass capillaries: A critical examination of the Washburn equation. Journal of Colloid and Interface Science 2013,411, 257. (34) Imanishi, K.; Einaga, Y., Effects of Hydrophilic Chain Length on the Characteristics of the Micelles of Pentaoxyethylene n-Decyl C10E5 and Hexaoxyethylene n-Decyl C10E6 Ethers. The Journal of Physical Chemistry B 2005,109 (15), 7574. (35) Zhuravlev, L. T., The surface chemistry of amorphous silica. Zhuravlev model. Colloids

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Figure 1. Schematic of experiment set up.

19

(a) (b)

Figure 2. AFM tomographic image of unmodified capillary tube surface (hydrophilic one).

20

(a) (b)

Figure 3. AFM tomographic image of TMCS modified capillary tube surface (hydrophobic one).

21

Figure 4. Images captured from high speed camera video show the motion of liquid meniscus in

capillary tube.

22

(a) (b)

(c)

Figure 5.Experimental results of liquids penetrating into hydrophilic capillary glass tube for

radius of 0.34 mm (a), 0.45 mm (b), and 0.56 mm (c).

23

(a) (b)

(c)

Figure 6. Experimental results of liquids penetrating into hydrophobic capillary glass tube for

radius of 0.34 mm (a), 0.45 mm (b), and 0.56 mm (c).

24

Figure 7. Equilibrium height as a function of ethanol volume ratio on hydrophilic and

hydrophobic surface. Solid dots are hydrophilic capillary tube, and open dots are hydrophobic

capillary tube.

25

(a)

(b)

Figure 8. Comparing penetrating experiment results with Eq. (1) calculation using equilibrium

contact angle in (a) hydrophilic capillaries and (b) hydrophobic capillaries when tube size is 0.34

mm in radius.

26

(a)

(b)

Figure 9. Variation of dynamic contact angle vs capillary number for different water/ethanol

liquid in three size glass tube 0.34 mm, 0.45 mm, and 0.56 mm for (a) hydrophilic and (b)

hydrophobic.

27

Figure 10. Wetting force as a function of the ethanol volume ratio in liquid on hydrophilic and

hydrophobic surfaces at time t = 0 s when tube radius is 0.34 mm.

28

Table 1. Physical properties measuring results of water/ethanol mixtures by volume fraction at

20°C in atmosphere.

Liquid Water

80% Water

& 20%

Ethanol

60% Water

& 40%

Ethanol

40% Water

& 60%

Ethanol

20% Water

& 80%

Ethanol

Ethanol

Density

と(103 kg/m3) 0.9982 0.9733 0.9460 0.9043 0.8551 0.7884

Viscosity µ

(10-3Pa•s)

1.002 1.9316 2.7917 2.7855 2.1807 1.144

Surface

tension け

(10-3 N/m)

72.75 41.48 32.47 27.76 24.87 22.27